Unity is home to oil fields that have been abandoned due to fighting.
The clash between Riek Machar's loyalists and government forces occurred early on Monday in Nhialdiu, a village close to the town of Bentiu which has changed hands repeatedly since a civil war began nearly four years ago.
"The number of the bodies that were found on the ground were 25," said Lam Tungwar, information minister for Northern Liech state, adding that the attack was "repulsed".
Those killed during the fighting included women, elderly people and local police officers, Lam Tungwar, state minister of information for Northern Liech, told Reuters news agency.
Lam Paul Gabriel, a spokesman for the SPLA-IO fighters, confirmed the clash, claiming "a successful operation" in which "the gallant SPLA-IO forces took control of Nhialdiu", killed 19 government soldiers and seized dozens of weapons.
Tungwar said most of the dead were civilians.
Dickson Gatluak Jock, military spokesman for South Sudanese Vice President Taban Deng Gai, said the attack coincided with dialogue in Nhialdiu between rival clans aimed at securing peace in the region.
A peace accord was signed in August 2015 and Machar returned to the capital in April last year to share power with Kiir.
However, the deal fell apart less than three months later, and Machar and his supporters fled the capital, Juba.
Tens of thousands of people have been killed and more than 3.5 million have been displaced since the conflict began.
The war has created what has been called one of the world's fastest-growing refugee crises, and both sides of the conflict have been accused of abuses.
Source: News agencies